Static metrics on spacetime manifolds with nonzero first Betti number, such as an infinite rotating cylinder, give a family of solutions that are locally the same but globally distinct in a gravitational analogue of this effect reported by John Stachel. Resistance oscillations as a function of magnetic flux were observed in nanotubes by Bachtold as a consequence of this effect. This phenomenon emerges from gauge invariance much as charge quantization emerges from the existence of magnetic monopoles. Its magnetic type gives a phase shift proportional to the path integral of the vector potential sometimes named for Berry, and it is usually observed following a particle's motion around a solenoid, and it was verified when it was observed that the interference pattern 
Static metrics on spacetime manifolds with nonzero first Betti number, such as an infinite rotating cylinder, give a family of solutions that are locally the same but globally distinct in a gravitational analogue of this effect reported by John Stachel. Resistance oscillations as a function of magnetic flux were observed in nanotubes by Bachtold as a consequence of this effect. This phenomenon emerges from gauge invariance much as charge quantization emerges from the existence of magnetic monopoles. Its magnetic type gives a phase shift proportional to the path integral of the vector potential sometimes named for Berry, and it is usually observed following a particle's motion around a solenoid, and it was verified when it was observed that the interference pattern of a beam of uniform energy electrons had changed. For 10 points, name this phenomenon predicted by Ehrenberg and Siday in which a charged particle in a region where the B and E fields are excluded is nonetheless affected by the vector potential.
Static metrics on spacetime manifolds with nonzero first Betti number, such as an infinite rotating cylinder, give a family of solutions that are locally the same but globally distinct in a gravitational analogue of this effect reported by John Stachel.
Ehrenberg-Siday-{Aharonov}-{Bohm} effect